Dynamics of chaotic driving: rotation in the restricted three-body problem

We investigate the rotation of a small nonspherical body in the planar restricted three-body problem along periodic, quasi-periodic, and chaotic orbits of the small body's center of mass. The rotation dynamics is chaotic in all three cases, but a systematic overview of it via stroboscopic mappings is possible only in the periodic case. We propose to explore the structured phase space patterns by following an ensemble of trajectories, a droplet, in the phase space. The temporal evolution of the pattern can be characterized by a time-dependent fractal dimension. It is shown to converge exponentially to a time-independent value for long times. In the presence of dissipation, the droplet typically converges to a so-called snapshot chaotic attractor whose shape might change chaotically in time, but whose asymptotic fractal dimension is constant.